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Phase transitions and magnetic domain coexistence in Nd0.5Sr0.5MnO3 thin films
We present a study of the physical properties of perovskite oxide Nd0.5Sr0.5MnO3 (NSMO) thin films grown on (110)-oriented SrTiO3 substrates. In bulk form, NSMO displays coupled magnetic and electronic transitions from paramagnetic/insulator to ferromagnetic (FM)/metal and then to antiferromagnetic (AFM)/charge-ordered insulator with decreasing temperature. In thin films, the AFM ordering only occurs when the films exist in an anisotropic strain state such as those obtained on (110)-oriented cubic substrates. In this work, resonant X-ray reflectivity, soft X-ray photoemission electron microscopy (X-PEEM), and magnetometry measurements showed that the NSMO film displays both vertical and lateral magnetic phase separation. Specifically, the film consists of three layers with different density and magnetic properties. The FM and AFM properties of the main NSMO layer were probed as a function of temperature using soft X-ray magnetic spectroscopy, and the coexistence of lateral FM and AFM domains was demonstrated at 110 K using X-PEEM
Heat-like and wave-like lifespan estimates for solutions of semilinear damped wave equations via a Kato's type lemma
In this work we consider several semilinear damped wave equations with “subcritical” nonlinearities, focusing on studying lifespan estimates for energy solutions. Our main concern is on equations with scale-invariant damping and mass. By imposing different assumptions on the initial data, we prove lifespan estimates from above, distinguishing between “wave-like” and “heat-like” behaviours. Furthermore, we conjecture logarithmic improvements for the estimates on the “transition surfaces” separating the two behaviours. As a direct consequence, we reorganize the blow-up results and lifespan estimates for the massless case, and we obtain in particular improved lifespan estimates for the one dimensional case, compared to the known results. We also study semilinear wave equations with scattering damping and negative mass term, finding that if the decay rate of the mass term equals to 2, the lifespan estimate coincides with the one in a special case of scale-invariant damped equation. The main tool employed in the proof is a Kato's type lemma, established by iteration argument
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